1. 08/06/2015 1 Beam Polarization at FCC-ee

2. 2 Transverse polarization both in the Z resonance region : 44 to 47 GeV beam energy, around half integer spin tunes)  m Z,  Z and in the WW thrshold region: 80 to 82 GeV also at half integer spin tunes)  m W is at the heart of the precision FCC-ee physics program. In fact it is one of these things that makes it very special wrt to hadronic or linear colliders or smaller e+e- storage ring colliders such as CEPC. It needs to be used continuously for both the W and Z mass measurements. A measurable polarization of a few percent is needed at both energies to proceed to spin matching to bring polarization level to ~10% that allows resonant depolarization. Physics requirement 08/06/2015

3. Koratzinos has revisited the uncertainties and the method to understand how much better we can do.  50 KeV typically for many measurements Issues: -- obtain polarization fast enough (need wigglers) -- ‘polarized single bunches’ with ‘top-off injection’ -- spin match all imperfections -- address kicks... and no e+ polarimeter!

4. To depolarize we must polarize and that is the hard part.

5. Polarization basics Polarization builds up by Sokolov Ternov effect (magnetic moment aligns on magnetic field by emission of Synchrotron radiation) B  se+se+ se-se- -- spin of e+ and e- are transverse and opposite -- polarization growth is slow f 0 = revolution frequency = c/C I 3 = 2  /  2 in other words, the polarization time scales as C 3 / E 5 C : Circumference  : bending radius at given energy polarization time is ~27 times longer at TLEP than LEP ~ 190 hours at the Z peak (45.5 GeV)

6. Its all about depolarizing effects depolarization occurs because the B field is not uniformly perpendicular to the storage ring plane. Transverse components ‘trip’ the spin by an amount  spin =  trajectory = 103.5 at the Z pole this is a problem because 1. the equilibrum spin is not the same for different energies in the beam 2. the equilibrium is not the same across the beam phase space  spread of equilibrium direction and excitation of spin resonances. Geometric kinks will generate an energy-dependent problem

7.  is the spin-orbit coupling i.e. the variation of the equilibrium spin direction upon a change of energy by SR in a magnet. The average can be expressed as a sum over the magnets. with The polarization time is reduced in the same way as the asymptotic polarization

8. What we know from LEP on depolarizing effects http://dx.doi.org/10.1063/1.1384062 AIP Conf. Proc. 570, 169 (2001) Spin 2000 conf, Osaka

9. can be improved by increasing the sum of |B| 3 (Wigglers) can be improved by ‘spin matching’ the sources of depolarization can be separated into harmonics (the integer resonances) and/or into the components of motion: receipes: -- reduce the emittances and vertical dispersion   this will be done at TLEP to reduce beam size! -- reduce the vertical spin motion  n  harmonic spin matching -- do not increase the energy spread

10. examples of harmonic spin matching (I) Deterministic Harmonic spin matching : measure orbit, decompose in harmonics, cancel components near to spin tune. NO FIDDLING AROUND. This worked very well at LEP-Z and should work even better at TLEP-Z if orbit is measured better.

11. When all else fails, empirical spin matching: excite harmonics one by one to measure directly their effect on polarization and fit for pole in 4-D space. Here 8% polarization at 61 GeV. WAS NOT EASY. examples of harmonic spin matching (II)

12. The energy spread really enhances depolarization

13. effect of energy spread on Polarization in a given machine was studied using the damping wigglers

14.  E  E b 2 /  The good news is that polarization in LEP at 61 GeV corresponds to polarization in FCC-ee at 81 GeV (80km ring) or 84.5 GeV (100km ring)  Not easy, but good news for M W measurement

15. Energy spread (Jx=1) LEP FCC-ee beam energy sigma(E) tau_P sigma(E) tau_P 45 GeV no wiggs 32 MeV 5.5 hrs 18 MeV 167 hrs 45 GeV wigglers 46 MeV 2.4 hrs 58 MeV 12 hrs 55 GeV no wiggs 48 MeV 1.96 hrs 26 MeV 61 hrs 61 GeV no wiggs 59 MeV 1.1 hrs 33 MeV 36 hrs 81 GeV 58 MeV 8.9 hr consider somewhere between 48 and 58 MeV as maximum acceptable for energy spread*). Take 52 MeV for the sake of discussion. Note that wigglers make energy spread worse faster at TLEP (damping is less) There is no need for wigglers at 81 GeV, but rather low level of polarization expected.   annoyingly: with wigglers at TLEP, the energy spread is larger than at LEP, for a given polarization time.

16. 08/06/2015 16 Eliana Gianfelice has started spin simulations at the Z energy with good prospects without and even with wigglers. Given the progress made since LEP on orbit corrections prospects are quite encouraging both at Z and W energies. ALL ASSUMING A PLANAR RING!

17. 17 KINKS 08/06/2015

18. 18 The high value of spin tune combined with the stochastic energy variations of particles due to synchrotron radiation  horizonal component of spin is destroyed in typically a few longitudinal damping times, in a way which is related to the energy spread.  Only the component of the spin that is parallel to the magnetic field is conserved  in case of a kink there is a continuous (twice per turn) change of the axis of the magnetic field which kicks the spin in the horizontal plane and would lead to immediate depolarization if uncorrected.  it is essential to compensate locally the spin rotation due to the kink with a bona fide spin rotator. This compensation has to be effective for any beam particle -- within the energy acceptance and -- within the transverse emittance. The KINK problem, an explanation with words: 08/06/2015

19. 19 spin normally orients itself opposite to magnetic field, for electrons. 08/06/2015

20. 20 POSSIBLE CORRECTION: 1. Example of compensation of a known imperfection that creates depolarization. 2. an idea of a possible correction scheme 3. discussion, warning. 08/06/2015

21. 21 Example: experimental solenoid compensation at LEP 08/06/2015

22. small spin rotator Spin matching bumps were double-pi bumps 22 Double pi bumps: vertical orbit and vertical dispersion cancel except inside bumps themselves. B 08/06/2015 Note that solenoids make poor spin rotators: need 250 T.m for 90degrees.

23. from LEP to FCC-ee 1. Double pi bumps worked very well at LEP. There was a particular relationship between vertical phase advance and spin tune. This has to be studied again before concluding that scheme can work for FCC-ee 2. the same principle (2 pi bumps) as for solenoids was used for harmonic and empirical spin compensation 3. and can be used in principle to spin-match small vertical orbit kicks (<1mrad). For the kinks for FCC -- this may or may not work for achieving a large (> 10mrad) orbit kick by decomposing it into several small ones 23 08/06/2015

24. 24 top view Artist view side view arc bends interspaced with vertical bends vertical kicks interspaced with arc bends Can one design kicks so that spin motion cancels? The butterflya single kick of 10mrad is way too large to swallow... break it up 08/06/2015

25. 25 top view side view spin view wrt trajectory Case of a kink of 0.8% split in two pieces, for s = 103.5 Horizontal bends Vertical bends  kink =0.4%=4mrad 0.4%  spin = 414 mrad  spin =   spin = 414 mrad what we would like: 08/06/2015

26. 26 in FCC-ee such a geometry would be about 700 m long at Z and 400 m at W. Hopefully can use in part the vertical kick magnets themselves.

27. 27 Comments on this simple scheme, assuming it can be realized in practice: 1. cancellation of spin precession in the vertical bend is ensured by precession in the interleaved horizontal bend 2. this cancellation will be affected by synchrotron radiation inside the system which changes one or two of the precession angles.  given the large radius of FCC-ee expect this to be small. TBV 3. it will also become less precise if particle is off-momentum 4. it will work better if kinks are smaller, keeping even number of kinks -- depolarization scales as  2. 5. it will only work for a precise beam energy. 6. for small changes of energy (such as a few percent changes) it should be feasible to correct mismatch with a small double pi bump 7. this and similar schemes will not work at the WW energy if it works at the Z and vice versa.This is a fundamental difficulty. 08/06/2015

28. 28 Investigation of practical implementation Bastian in Washington. one such cell bends by 0.4% if B rotated by 90 o... This FODO cell bends by 4.08 mrad  spin is rotated by 0.422 at Z, 0.745 at W pi rotation is realized with 7.44 such cells at v s = 103.5 (Z peak) pi rotation is realized with 4.22 such cells at v s = 182.5 (WW) pi bump in vertical space is realized with 3 such cells 08/06/2015

29. 29 AT THIS POINT: 1. Kinks in the Arcs of FCC produce VERY LARGE spin rotations. -- a 1.7% kink at 80.5 GeV (WW) simply flips the spin. 2. Uncorrected, this would result in 0.0% polarization at all energies of interest. 3. There is an almost thinkable solution at the Z with splitting the kick bends in an even number of segments in such a way that the there is a pi spin rotation between them. (assuming the imperfect pi rotation in 8 cells can be fixed, e.g. switching off two of the 32 bends or decreasing them by 6% or...) 4. There is an almost thinkable, but different solution at the WW (assuming the imperfect pi spin rotation in 4 cells can be fixed, e.g. by increasing strength by 5% or....) 5. I have no clue at the moment on how to unify the spin compensation for Z and WW to keep the same tunnel/vac. chamber geometry. Perhaps using orbit correctors to complement the system ? Hera used a variable spin rotator on a smaller relative energy range. 5’ I have not envisaged the effect on vertical emmittance. 08/06/2015

30. 30 KINKS AT THIS POINT: 6. to go one step further one would need -- implementation of FCC-ee lattice in the spin simulators -- start to play with the correctors to find the ‘elementary spin rotator’ (the equivalent of the pi bump of LEP) -- see if they can help with the problem. -- otherwise try to design a full-fledge set of *variable* spin rotators on each side of each kink. 7. In any case : -- needs to worry about spin tune shifts at ppm level. -- concern with kinks at W energy which will be already delicate. -- no point in having polarization at only one of the two energies. -- increase of the number of magnets and of the strength of the horizontal bending magnets would result in an increase of energy loss per turn. This would require more GVolts and more MW, for main ring and injector, thus more cost -- to be considered in the analysis. 08/06/2015

31. 31 Conclusions Transverse polarization for energy calibration is a key element of the precision measurement program of m Z and m W at FCC-ee. It needs to be used continuously for both the W and Z mass measurements. The prospects for natural Sokolov Ternov polarization are good, given the smaller energy spread with the large ring, and given the progress in orbit corrections, for a PLANAR ring. At the Z peak polarization wigglers are needed and feasible. At the W energy small but useable level of polarization is expected, without wigglers. KINKS of.4% to 1.7% induce large spin rotations and must be corrected locally. Solutions can be imagined for either energy (but have not been worked out yet) No solution has been found at this point that compensates kinks both at Z and WW while keeping the same tunnel/vac. chamber geometry Potentially a show-stopper.